Analytic torsion and closed geodesics on hyperbolic manifolds

1986 ◽  
Vol 84 (3) ◽  
pp. 523-540 ◽  
Author(s):  
David Fried
Keyword(s):  
Hyperbolic Manifolds ◽  
Analytic Torsion ◽  
Closed Geodesics

scholarly journals Analytic torsion of complete hyperbolic manifolds of finite volume

2012 ◽  
Vol 263 (9) ◽  
pp. 2615-2675 ◽  
Author(s):  
Werner Müller ◽  
Jonathan Pfaff
Keyword(s):  
Finite Volume ◽  
Hyperbolic Manifolds ◽  
Analytic Torsion

scholarly journals Exponential mixing of frame flows for convex cocompact hyperbolic manifolds

2021 ◽  
Vol 157 (12) ◽  
pp. 2585-2634
Author(s):  
Pratyush Sarkar ◽  
Dale Winter
Keyword(s):  
Asymptotic Formula ◽  
Error Term ◽  
Arbitrary Dimension ◽  
Hyperbolic Manifolds ◽  
Closed Geodesics ◽  
Technical Result ◽  
Exponential Mixing ◽  
Spectral Bound ◽  
Matrix Coefficients ◽  
Convex Cocompact

The aim of this paper is to establish exponential mixing of frame flows for convex cocompact hyperbolic manifolds of arbitrary dimension with respect to the Bowen–Margulis–Sullivan measure. Some immediate applications include an asymptotic formula for matrix coefficients with an exponential error term as well as the exponential equidistribution of holonomy of closed geodesics. The main technical result is a spectral bound on transfer operators twisted by holonomy, which we obtain by building on Dolgopyat's method.

scholarly journals Anomalies and analytic torsion on hyperbolic manifolds

1999 ◽  
Vol 40 (8) ◽  
pp. 4119-4133
Author(s):  
A. A. Bytsenko ◽  
A. E. Gonçalves ◽  
M. Simões ◽  
F. L. Williams
Keyword(s):  
Hyperbolic Manifolds ◽  
Analytic Torsion

scholarly journals A GLUING FORMULA FOR THE ANALYTIC TORSION ON HYPERBOLIC MANIFOLDS WITH CUSPS

2015 ◽  
Vol 16 (4) ◽  
pp. 673-743 ◽  
Author(s):  
Jonathan Pfaff
Keyword(s):  
Asymptotic Behaviour ◽  
Eisenstein Series ◽  
Hyperbolic Manifold ◽  
Hyperbolic Manifolds ◽  
Analytic Torsion ◽  
Arithmetic Groups ◽  
Reidemeister Torsion ◽  
Cohomology Of Arithmetic Groups ◽  
Gluing Formula

For an odd-dimensional oriented hyperbolic manifold with cusps and strongly acyclic coefficient systems, we define the Reidemeister torsion of the Borel–Serre compactification of the manifold using bases of cohomology classes defined via Eisenstein series by the method of Harder. In the main result of this paper we relate this combinatorial torsion to the regularized analytic torsion. Together with results on the asymptotic behaviour of the regularized analytic torsion, established previously, this should have applications to study the growth of torsion in the cohomology of arithmetic groups. Our main result is established via a gluing formula, and here our approach is heavily inspired by a recent paper of Lesch.

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